Abstract
An abstract version of the programmed iteration method (used in the theory of differential games) is considered that is intended for the problem of observing phase constraints on a nonempty subset of the real line. It is assumed that trajectories and uncontrolled disturbances are realized in packages of mutually inconsistent spaces. This consistency is postulated to investigate solvability conditions for the problem in the class of quasi-strategies. As a result, the set of successful solvability is constructed and the structure of resolving strategies is determined.
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